1

Interfacial Properties of Bilayer and Trilayer Graphene on Metal

Substrates

Jiaxin Zheng,1,2,†

Yangyang Wang,1, †

Lu Wang,3 Ruge Quhe,

1,2 Zeyuan Ni,

1 Wai-Ning

Mei,3 Zhengxiang Gao,

1 Dapeng Yu,

1 Junjie Shi,

1 and Jing Lu

1,*

1State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking

University, Beijing 100871, P. R. China

2Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871,

P. R. China

3Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0266

†These authors contributed equally to this work.

*Corresponding author: jinglu@pku.edu.cn

One popular approach to prepare graphene is to grow them on transition metal substrates

via chemical vapor deposition. By using the density functional theory with dispersion

correction, we systematically investigate for the first time the interfacial properties of bilayer

(BLG) and trilayer graphene (TLG) on metal substrates. Three categories of interfacial

structures are revealed. The adsorption of B(T)LG on Al, Ag, Cu, Au, and Pt substrates is a

weak physisorption, but a band gap can be opened. The adsorption of B(T)LG on Ti, Ni, and

Co substrates is a strong chemisorption, and a stacking-insensitive band gap is opened for the

two uncontacted layers of TLG. The adsorption of B(T)LG on Pd substrate is a weaker

chemisorption, with a band gap opened for the uncontacted layers. This fundamental study

also helps for B(T)LG device study due to inevitable graphene/metal contact.

2

Introduction

Graphene has become a ‘hot topic’ due to its extraordinary properties1-3

and wide range

of possible applications4-8

. Synthesis of high-quality graphene on a large scale is the

foundation for its application. Among different preparation methods, growing graphene on

transition metals including Cu9-14

, Co15

, Ni16,17

, Pt18

, Pd19

, Au20

, Ru21,22

, Rh23

, and Ir24,25

via

chemical vapor deposition (CVD) is overwhelming because of high-quality, low preparation

temperature, scalable production, and easy transfer to other substrates. Through CVD method,

not only single layer graphene (SLG) but also few-layer graphene can be synthesized13,14,16

.

Among few-layer graphene, bilayer (BLG) and trilayer graphene (TLG) are the most

extensively studied materials, partially due to the fact that there is an electrically tunable band

gap in BLG26-30

and ABC-stacked TLG31-34

and meanwhile the carrier mobility is not degraded,

which are critical for their application in transistor. Additionally, in an actual device,

graphene has to be contacted with metal electrode. Therefore, the interfacial properties of

B(T)LG and metal contacts should be clarified.

The interfacial properties between SLG and metals have been systematically

studied23,35-38

. The adsorption of SLG on Al, Ag, Cu, Au, and Pt (111) surfaces is a weak

physisorption, which preserves the Dirac cone of SLG. By contrast, the adsorption of SLG on

Ti (0001) surface, and Ni, Co, and Pd (111) surfaces is a strong chemisorption, which perturbs

the electronic structure of SLG significantly. SLG is n-type doped by Al, Ag, Cu, Ti, Co, Ni

and Pd, but p-type doped by Au and Pt. However, a systematic study on the interfacial

properties between B(T)LG and metal substrates is lacking and leaves three fundamental

issues open: (1) How do the B(T)LG/metal interfacial properties change with the species of

metals? In view of the additional layer and easier break of inverse symmetry, new features

may emerge when BLG and ABC-stacked TLG are contacted with metal substrates compared

with SLG cases. (2) How do the TLG/metal interfacial properties depend on the stacking style

of TLG? The second issue becomes especially crucial in light of the fact that the ABC- and

ABA-stacked TLG possess inversion and mirror symmetries, respectively, resulting in a

distinct response to electric field: A vertical electric field can open a band gap in ABC-stacked

TLG but increase the overlap between the conduction and valence bands in ABA-stacked

TLG instead31-34,39

. (3) Previous theoretical studies have been reported that the contact effects

3

between SLG and Al electrodes can affect the transport properties of SLG devices

significantly by inducing an extra conductance minimum at the Dirac point of the contacted

region and giving rise to an electron-hole asymmetry40

. It is open how the metallic contacts

affect the transport properties of B(T)LG devices.

In this Article, we provide the first systematic investigation on the interfacial properties

of BLG and TLG on a variety of metals (Al, Ag, Cu, Au, Pt, Ti, Co, Ni, and Pd) by using the

density functional theory (DFT) with dispersion correction and establish the general physical

picture of the B(T)LG/metal interfaces. Three categories of B(T)LG/metal interfacial

structures are revealed in terms of the adsorption strength and electronic properties: The

adsorption of B(T)LG on metal substrates (Al, Ag, Cu, Au, and Pt) is a weak physisorption in

the first category of interfaces, but a band gap can be opened and its size depends on the

possessed symmetries in graphene. The adsorption of B(T)LG on metal substrates (Ti, Ni, and

Co) is a strong chemisorption in the second category of interfaces, and bands of the upper

layer graphene of BLG are intact while a stacking-insensitive band gap is opened for the two

uncontacted layers of TLG. The adsorption of B(T)LG on metal substrates (Pd) in the third

category of interfaces is a weaker chemisorption, with a stacking-sensitive band gap opened

for the two uncontacted layers of TLG and a band gap of 0.12 eV opened for the upper layer

graphene of BLG. Finally, we design a two-probe model made of BLG contacted with Al and

Ti electrodes, respectively, and calculate their transport properties by using ab initio quantum

transport theory. Distinct transport properties are observed: A clear conductance gap rather

than a conductance minimum appears at the Dirac point of the contacted region with Al as

electrodes but this gap is full filled with Ti as electrodes.

Results

Geometry and stability of B(T)LG on metal substrates

The most stable configurations of the SLG/metal interfaces are shown in Figure 1a

(metal = Co, Ni, and Cu, named after top-fcc interface) and 1b (metal = Al, Ag, Pt, Au, and

Ti)35,36

. We choose the two configurations as the initial configuration of B(T)LG/metal

contacts. As shown in Figure 1c and d, TLG/metal contacts favor split alignment of the first

graphene layer with respect to metals compared with those of the S(B)LG/metal contacts.

4

The calculated key data are presented in Table 1. The binding energy Eb of the

B(T)LG/metal contact is defined as

Eb = (EG + EM – EG/M)/N (1)

Where EG, EM, and EG/M are the relaxed energy for B(T)LG, the clean metal surface, and

the combined system, respectively, and N is the number of carbon atoms in a unit cell. The

interfacial distance dC-M is defined as the average distance of innermost graphene to metal

surfaces. The B(T)LG/metal contacts can be classified into three categories according to the

binding strength and the interfacial distance. In the first category of interfaces (Al, Ag, Cu,

Au, and Pt (111) substrates), B(T)LG are physisorbed on these metal substrates with smaller

binding energies of Eb = 0.032 – 0.063 eV and larger interfacial distances of dC-M = 3.13 –

3.53 Å; for TLG both quantities are insensitive to the stacking order. With larger Eb = 0.094 –

0.210 eV and smaller dC-M = 2.04 – 2.34 Å, B(T)LG are strongly chemisorbed on Ti (0001)

surface, and Ni and Co (111) surfaces, forming the second category of interfaces. Differently,

the binding in the second category of interfaces is always stronger by 0.02 – 0.03 eV for the

ABC stacking style compared with the ABA stacking style. The adsorption of the third

category of interfaces (Pd substrate) is a weak chemisorption (or strong physisorption), which

is intermediate between the physisorption and strong chemisorption, with Eb = 0.08, 0.085,

and 0.103 eV and dC-M = 2.70, 2.54, and 2.50 Å for BLG, ABA-, and ABC-stacked TLG,

respectively. The same classification is applicable to the SLG/metal contacts35,36

, and thus

the graphene layer number has little effect on the adsorption categories. The flat planes of

BLG and TLG are all kept in the first category of interfaces. But the innermost graphene layer

buckles slightly with buckling heights of 0.01 – 0.11 Å in the second category of interfaces

and 0.01 – 0.02 Å in the third category. The buckling height difference also reflects the

difference of interaction strength among three categories of interfaces.

Electronic structure of BLG on metal substrates

The classification is also in accordance with the electronic structure of B(T)LG on metal

surfaces. We calculate the band structures of the first category of interfacial structures. As

showed in Figure 2, the band structure of the BLG can be clearly identified in these systems

because of the weak interaction. Two important changes in the BLG bands are noteworthy:

5

One is the Fermi level (Ef) of BLG is shifted upward or downward when contacted with the

first class of metal surfaces, similar to SLG cases 35,36

. BLG is n-type (upward shift) doped

when contacted with Ag, Al, and Cu but p-type doped (downward shift) when contacted with

Au and Pt. This phenomenon can be attributed to the different work functions of BLG (WG,

the calculated value is 4.58 eV)) and metal surface (WM). The Fermi level shift is defined as

ΔEf = Ef – ED, where ED is the middle energy of the band gap of the BLG adsorbed on metal

substrates. The Fermi level shift ΔEf as a function of (WM – WG) is plotted in Figure 3(a). The

change tendency of ΔEf with (WM – WG) is in accordance with that of the SLG cases35,36

. The

crossover point from n- to p-type doping is not at WM – WG = 0 but at about WM – WG = 0.4

eV (the LDA result for the SLG cases is WM – WG = 0.9 eV) 35,36

. At the crossover point, there

is no charge transfer between metal and BLG. Therefore, the value of WM – WG at that point

reflects the potential step resulting from the BLG-metal chemical interaction (Δc = 0.9 eV).

Such a chemical interaction effectively reduces WM by Δc. As a result, a larger WM is needed

to induce p-type doping in both BLG and SLG.

The other feature of the electronic structures of BLG in the first class of interfaces is the

appearance of a band gap of Eg = 0.102 – 0.200 eV (Table 1), which is absent in their SLG

counterparts. These band gaps are smaller than the maximum band gap of 0.25 eV opened in

BLG under a vertical electric field29,41

and the maximum band gap of 0.34 eV opened in SLG

sandwiched between hexagonal boron nitride under a vertical electric field42

. The mechanism

of band gap opening can be explained by a BLG/metal contact model, as shown in Figure 3(b).

We use Δn, Δn1, and Δn2 to denote the transferred charge on metal surfaces, the bottom layer

graphene, and the upper layer graphene, respectively. The electron transfer assumedly creates

a uniform electric field E and E1 between the sheets. The potential difference between the

two graphene sheets is

ΔU = U2 − U1 = −αΔn2– Δc, α = e2d0/ε0κ (2)

where ε0 is the dielectric constant of vacuum and κ the relative dielectric constant of graphene.

ΔU is thus proportional to the transferred charge on the upper layer graphene. Due to ΔU ≠ 0,

the inversion symmetry of A-B stacked BLG is broken. As a result, a band gap is induced,

which has been confirmed by the tight-binding calculations in the system of depositing

potassium on BLG43

and in few layer graphene under a vertical electric field32,44,45

. The

6

change of the band gap Eg as a function of ΔEf is shown in Figure 3(c). Eg increases with the

increasing |ΔEf| in both the n- and p-type doping regions. The cause lies in the fact with the

increasing doping level in the n-type doping region (reflected by |ΔEf|), the more charge is

transferred, and |Δn2| and |−αΔn2 – Δc| gets larger, leading to a larger |ΔU| and thus a larger Eg.

The Eg – ΔEf data in the n-type doping region even can be roughly fitted by a linear function

Eg = – 0.42 × ΔEf + 0.05 eV (black dashed line). It implies that there is a band gap of 0.05 eV

for BLG physisorbed on metal substrates due to Δc even if the doping level is zero.

Experimentally, the current on/off ratio of a BLG field effect transistor (FET) is

significantly improved by one order of magnitude when the channel BLG is deposited by Al,

suggestive of opening of a transport gap in BLG46

. This result is in agreement with our

calculation that a band gap is opened for BLG on Al substrate. Furthermore, in terms of our

calculations, the current on/off ratio of BLG FETs can also be improved by deposition of Cu,

Ag, Au, and Pt on channel BLG.

The band structures of the second category of interfaces are shown in Figure 4(a-e). The

bands of the bottom layer graphene are strongly disturbed and hybridized with the d bands of

the metal surfaces, and the characteristic cone at the K point is destroyed. The minority spin

bands of Ni and Co hybridize with both the π and π* bands of the bottom layer graphene,

whereas the majority spin bands of Ni and Co hybridize chiefly with the π bands of the

bottom layer graphene, because some of the minority spin bands are above the Dirac point of

graphene while most of the majority spin bands are below the Dirac point. The 3d bands of Ti

hybridize with both the π and π* bands of the bottom layer graphene because they are

distributed widely both below and above the Dirac point. The hybridization between Ti and

the bottom graphene is so strong that we even can’t identify the bands of the bottom layer

graphene, a result consist with the largest binding energy of BLG on Ti. By contrast, the band

structure of the upper layer graphene is almost intact and can be clearly identified, and the

Dirac cone at the K point is preserved perfectly. The only change is that Ef of the upper layer

graphene is shifted upwards, induced an n-type doping. The Fermi-level shift of the upper

layer graphene is −0.364/−0.280 eV (−0.428/−0.381 eV) for the bands of the

majority/minority spin of Ni (Co), respectively, and −0.283 eV for the bands of Ti contact

(Table 1). All these changes indicate that the bottom layer graphene has been strongly bonded

7

with the metal surfaces and formed a new surface. The interaction between the upper layer

graphene and this new surface is a physisorption, so the electronic structure of the upper layer

graphene is well preserved. Our band structure of BLG on Ni (111) surface is in agreement

with that reported by Gong et al.47

Another theoretical work shows that BLG is chemisorbed

on Ru (0001) surface, with an intact band structure for the upper layer graphene and a

strongly perturbed band structure for the bottom layer graphene22

; apparently, BLG/Ru (0001)

also belongs to the second class of interfaces.

The Fermi-level shift of the upper layer graphene on Ni (Co) substrate is −0.364/−0.280 eV

(−0.428/−0.381 eV) for the majority/minority spin bands, respectively (Table 1), which is

comparable with that (−0.361 eV) of BLG on Al substrate. But the work function of Co/Ni is

4.97/4.93 eV, and WCo/Ni – WG = 0.390/0.350 eV, very close to the crossing point WM – WG =

0.4 eV. It appears that the Fermi-level shift should be very small for Co (Ni) contact

according to our previous model. Nevertheless, the bottom layer graphene is strongly

chemisorbed on the Co (Ni) surface, and they actually form a new surface. The work function

of the new surface is Wnew = 4.33/4.32 eV (Co/Ni), and one has Wnew – WG = −0.250/−0.260

(Co/Ni). The Fermi-level shift of the upper graphene on Ni/Co substrate is ΔEf ~ 0.280 eV

from Figure 3(a), which well accounts for the actual values (−0.364/−0.280 eV for Ni and

−0.428/−0.381 eV for Co)

In Figure 4(f), we show the band structure of the third category of interfaces (BLG/Pd).

The conduction bands of the bottom layer graphene can be identified but it is hard to identify

the valence bands, indicating that the Pd 4d/5s bands are chiefly hybridized with the valence

bands of the bottom layer graphene because most of the Pd 4d/5s bands are below the Dirac

point of BLG. Similar to the second class of interfaces, the band structure of the upper layer

graphene can be clearly identified, but a band gap of 0.124 eV is opened. Ef of the upper layer

is shifted upward by 0.160 eV, indicative of n-type doping. This unique interfacial electronic

structure of BLG/Pd is ascribed to the fact that the intermediate interaction between BLG and

Pd surface preserves the partial electronic properties of the bottom layer and it does not

overwhelm the intrinsic graphene interlayer coupling. The dipole field induced by

Pd-graphene charge transfer breaks the inverse symmetry of the two graphene layers, and a

band gap is opened and is chiefly reflected in the upper layer graphene. The Eg – ΔEf datum of

8

BLG on Pd substrate falls in the Eg – ΔEf fitting curve for BLG physisorbed on metal

substrates in the n-doping region (Figure 3c).

Electronic structure of TLG on metal substrates

The electronic structures of the first category of TLG/metal interfaces are plotted in

Figure 5. It is clearly shown that the band structures of both ABA- and ABC-stacked TLG are

preserved, accompanied by a Fermi level shift and an opened band gap. The same as BLG

cases, TLG is doped with electrons by Al, Ag, and Cu contacts and with holes by Au and Pt

contacts. Table 1 summarizes the evolution of the Fermi-level shift ΔEf = ED – Ef and band

gap Eg of TLG. The Fermi-level shift ΔEf as a function of WM – WG is shown in Figure 6a for

ABA- and ABC-stacked TLG (WG is the calculated work function of TLG, 4.52 eV). The

crossover point from n- to p-type doping is about WM – WG = 0.56 for ABA-stacked TLG and

0.55 eV for ABC-stacked TLG.

Both the Fermi-level shift ΔEf and work function difference WM – WG are less sensitive to

the stacking order. However, the stacking order affects significantly the band gap of TLG:

ABA-stacked TLG has generally smaller band gaps of Eg = 0 − 0.061 eV while ABC-stacked

TLG has generally larger band gaps of Eg = 0 − 0.249 eV. The current on/off ratio of TLG

FET is expected to be increased by deposition of Al, Cu, and Ag on channel TLG due to a

band gap opening. As shown in Figure 6b and Figure S1, the sizes of the band gap of both

ABC- and ABA-stacked TLG rough linearly depend on ΔEf. The band gaps of ABC-stacked

TLG are apparently electron-hole asymmetric: they are significantly larger in the n-type

doping region (Eg = 0.181 – 0.249 eV) than those in the p-type doping region (Eg = 0 – 0.018

eV) at the same |ΔEf |. The band gaps of ABA-stacked TLG are slightly electron-hole

asymmetric: the band gaps are slightly larger in the n-type doping region (Eg = 0.032 – 0.061

eV) than those in the p-type doping region (Eg = 0 eV) given the same |ΔEf | (Figure S1). The

mechanisms of band gap opening in ABA- and ABC-stacked TLG and the reason of

electron-hole asymmetry in band gaps can also be explained with a TLG/metal contact model

(Figure S2).

The electronic structures of the second category of interfaces (TLG/Ti, Co, and Ni

contacts) are plotted in Figure 7. Similar to BLG cases, both the π and π* states of the

9

innermost graphene layer are strongly hybridized with the 3d states of Ti, and minority-spin

3d states of Co and Ni. Only the π states of the innermost graphene layer are strongly

hybridized with the Co and Ni majority-spin 3d states. The strongly coupled innermost

graphene layer serves as an active buffer and effectively passivates the metal d states at the

interface. As a result, the electronic structure of the two uncontacted layers is nearly intact

except that a band gap is opened, similar to the first category of interfaces for BLG/metal. The

band gaps of the uncontaced BLG are less sensitive to the stacking mode, with Eg = 0.100 −

0.229 eV, which approach the maximum band gap of freestanding BLG obtained from the

theoretical (0.25 − 0.28 eV)28,32

and experimental (0.25 eV)29

studies. The band gap opening

is attributed to a potential energy difference between the two uncontacted graphene layers,

which is ΔU32 = −αΔn3 −Δc′, where Δc′ is the potential step resulting from the interaction

between the second graphene layer and the chemically bonded innermost graphene-metal

system. Such a potential energy difference breaks the inversion symmetry of the two

uncontacted graphene layers, thus opening a band gap. TLG is n-type doped in both stacking

styles for the work function of the uncontaced BLG WG is larger than that of the new

graphene-metal surface Wnew.

The electronic structures of the third category of interfaces (TLG/Pd contact) are shown in

the second and fourth top panels of Figure 7. TLG is n-type doped by Pd substrate in both

stacking styles. Though the π states of the innermost graphene layer are perturbed strongly,

the π* states are only slightly affected, leading to BLG-like valence bands (two bands visible

near the K point) and TLG-like conduction bands (three bands visible near the K point). The

cause is the same as BLG cases: most of the Pd 4d states are below the Dirac point of

graphene and they can only hybridize with the π states of the innermost graphene layer.

Analogous to the physisorption cases, the band gap of the two uncontaced layers of TLG on

Pd substrate is strongly dependent on the stacking mode, with Eg = 0.064 and 0.308 eV for

ABA and ABC stacking styles, respectively. The latter band value is even marginally larger

than the maximum band gap of freestanding BLG under a uniform electric field obtained

from the theoretical (0.25 − 0.28 eV)28,32

and experimental (0.25 eV)29

studies and comparable

with the maximum band gap of SLG sandwiched between h-BN sheet under a uniform

electric field42

. The unique behavior of TLG/Pd is also agreement with the intermediate

10

binding between typical physisorption and chemisorption.

Transport properties of BLG contacted with metal electrodes

Finally, we further study how the interfacial properties affect the transport properties of

BLG devices when contacted with metallic Al and Ti leads. The two-probe model is

presented in Figure 8(a), and the distance between the Al/Ti lead and BLG is 3.45/2.18 Å,

according to our DFT results. The transmission spectrum of the device with Al electrodes is

shown in Figure 8(b), where a minimum (Dch) close to Ef due to the Dirac point of the channel

BLG and a 0.22eV gap at E – Ef = − 0.6 eV are observed. By contrast, there are only one

transmission minimum close to Ef for pure BLG without metal electrode (Inset in Figure 8(b))

and two transmission minima for SLG contacted with Al electrodes (one close to Ef, and the

other at E – Ef = − 0.6 eV due to the Dirac point of SLG in the lead) (Figure 8(c)). The

transport gap in Figure 8(b) originates from a gap of the same size in the projected density of

states (PDOS) of the BLG in the lead, as shown in Figure 8(d), because the transmission

coefficient of the device, T(E), is connected with the PDOS of the channel and the two

electrodes via the relation48:

ch L R

ch L ch R L R

( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( ) ( )

g E g E g ET E

g E g E g E g E g E g E

(3)

where gch(E) and gL/R(E) are the PDOS of the channel and the left/right lead, respectively.

Both gaps can be attributed to the band gap of Eg = 0.20 eV of corresponding infinite BLG

contacted with Al electrodes. The transmission spectrum with Ti electrodes is shown in Figure

8(e). Compared with Al contacts, the transmission minimum due to the Dirac point of the

channel BLG remains but the transmission gap is absent because the characteristic conical

point at the K point of the bottom layer graphene is destroyed. There is neither gap nor Dirac

point in the PDOS of BLG in the lead (Figure S3). From the transmission spectra, Ti electrode

can transport a larger current than Al electrode. In the light of similar interfacial properties of

TLG/metals to BLG cases, the same contact effect on transport properties of TLG devices as

BLG devices with Al and Ti electrodes is expected: Ti electrode can transport a larger current

than Al electrode. The difference in the transport properties between Al and Ti electrodes in

BLG is also reflected from a difference of the transmission eigenchannel at E – Ef = − 0.6 eV

11

and at the (π/3a, 0) point of the k-space. As displayed in Figure 8(f), the transmission

eigenvalue at this point nearly vanishes with Al electrodes, and the incoming wave function is

nearly completely scattered and unable to reach to the other lead. By contrast, the

transmission eigenvalue at the point is 0.96 with Ti electrodes, and the incoming wave

function is scattered little and most of the incoming wave is able to reach to the other lead.

Discussion

No band gap is detected experimentally for graphene on Pt18

and Au49

. However, band

gaps of 0.18, 0.25, and 0.32 eV are detected for graphene on Cu/Ni49

, Cu50

, and Ag/Ni49

substrates, respectively, in angle-resolved photoelectron spectroscopy (ARPES). If graphene

is identified as single layer one, these measurements are apparently in contradiction with the

calculated zero-gap for SLG on Cu and Ag substrates35,36,38

. One possible solution to such a

great discrepancy is to identify graphene as BLG or ABC-stacked TLG, since CVD growth on

Ni substrate can yield few-layer graphene with random stacking order16,17

and on Cu substrate

can yield bilayer12

and few-layer13,14

graphene, breaking the self-limiting nature of growth

process. According to our calculations, BLG on Cu, and Ag (111) surfaces has a band gap of

0.11, 0.13 eV, and ABC-stacked TLG has a band gap of 0.181 and 0.203 eV, respectively, all

of which are comparable with the measured values18,49,50

.

The other interesting point is the different strength of interaction in different categories

of interfaces. In terms of so-called d band model, the bond strength increases when moving to

left and up in the transition metal series51

. As moving from the right to the left, the d band

moves up in energy, the filling of d band decreases and the antibonding graphene-metal d

states become more depopulated, resulting in a strong bonding. Rises of the 3d, 4d, and 5d

states are observed as going from Ni, Co, to Ti, from Ag to Pd, and from Au to Pt,

respectively. From Table 1, we indeed have Eb (Ti) > Eb (Co) > Eb (Ni) > Eb (Cu) for 3d metals,

Eb(Pd) > Eb(Ag) for 4d metals and Eb(Pt) > Eb(Au) for 5d metals. The same binding

difference is available for SLG on metal substrate35,36

. Because the Ni and Co 3d states of the

minority-spin are higher in energy than those of the majority-spin (Figure 5), TLG should

interact more strongly with the minority-spin states of Ni/Co in terms of this model.

As moving down in one group, relativistic effects become more remarkable in the core

12

electrons, therefore the d-state orbitals of metals diffuse more widely, resulting in a worse

overlapping of graphene π states and metal d states and a weaker binding23

. Besides, the

strength of covalent bond generally decreases with the increase of the atomic radius in one

group. The calculated binding energy for group 10 metals (Ni, Pd, and Pt) with TLG indeed

follows this rule and we have Eb (Ni) > Eb (Pd) > Eb (Pt) (See Table 1). In fact, Ti, Pd, and Pt

are the three represents of the three classes of metals: BLG and TLG are strongly

chemisorbed on Ni, and weakly chemisorbed on Pd, while the adsorption of graphene on Pt

degenerates into a physisorption. The interaction strength change of graphene with group 9

metals Co, Rh, and Ir also obeys the same rule15,23-25

.

Epitaxial ABA-stacked TLG on Ru (0001) surface has been investigated by Sutter et al.22

The electronic structure determined by selected-area APPES shows BLG-like π band

dispersion. According to their DFT calculation, the two uncontacted graphene layers on Ru

(0001) surface behaves like freestanding BLG without a band gap though they are heavily

n-type doped (the top of the valence band is located at −0.30 0.05 eV below Ef). This

result is somewhat surprising because the potential difference induced by graphene-metal

electron redistribution will destroy the inversion symmetry of the two uncontacted graphene

layers. We therefore recalculated the ABA-stacked TLG/Ru contact using the same

parameters set by Sutter et al.22

The calculated electronic structure is shown in Figure S4. As

expected, a band gap of 0.127 and 0.147 eV is opened in both the CASTEP and VASP

calculations. The top of the valence band is located at −0.267 and −0.261 eV below Ef in the

CASTEP and VASP calculations (Supplementary information, Figure S4), respectively,

consistent with the micro-ARPES data −0.30 0.05 eV22

. We note that the DFT calculation

of Gong et al.47

for ABA-stacked TLG/Ni contact also found an energy gap of Eg = 0.133 eV

for the majority-spin band, comparable with our value of 0.191 eV. This calculation also

supports our results that the band gap of the uncontacted two layers is generally opened by the

charge redistribution between metal and TLG in the second category of interfaces.

In summary, we present the first systematic first-principles investigation on the

interfacial properties of BLG and TLG on a variety of metal substrates. According to the

adsorption strength and electronic properties, the BLG/metal and TLG/metal interfacial

structures can be classified into three categories. In the first category of interfaces, B(T)LG

13

are physisorbed on Al, Ag, Cu, Au, and Pt substrates; a band gap of 0.1 – 0.2 eV is opened for

BLG, and a stacking-sensitive band gap is opened for TLG, with the values of 0 − 0.061 and 0

− 0.249 eV for ABA- and ABC-stacking styles, respectively. In the second category of

interfaces, B(T)LG are chemisorbed on Ti, Ni, and Co substrates; the bands of the bottom

layer graphene is strongly perturbed, but those of the upper layer graphene of BLG is intact

and a stacking-insensitive band gap is opened for the two uncontacted layers of TLG. In the

third category of interfaces, B(T)LG are weakly chemisorbed on Pd substrate; a band gap of

0.12 eV is opened for the upper layer graphene of BLG and a band gap of 0.064 and 0.308 eV

is opened for the two uncontacted layers of ABA- and ABC-stacked TLG, respectively. An ab

initio quantum transport simulation is performed for a two-probe model made of BLG

contacted with Al or Ti electrodes. A transmission minimum and a transport gap are observed

in the transmission spectrum with Al contact. By contrast, there is only one transmission

minimum in the transmission spectrum with Ti contact due to the strong binding in the

electrodes. This fundamental study not only provides a deeper insight into the interaction

between B(T)LG and metal substrates but also helps to B(T)LG-based device study because

of inevitable B(T)LG/metal contact.

Methods

We use six layers of metal atoms (Ni, Co, Cu, Al, Ag, Cu, Pt, and Au) in (111) orientation

and Ti in (0001) orientation to simulate the metal surface, and a hexagonal supercell is

constructed with a BLG or TLG adsorbed on one side of the metal surface, as shown in Figure

1. We fix in-plane lattice constant of TLG to the experimental value a = 2.46 Å. The 11 unit

cells of Ni, Co, and Cu (111) faces are adjusted to graphene 11 unit cell, and 33 unit

cells of Ti (0001) face and Al, Ag, Cu, Pt, and Au (111) faces are adjusted to graphene 22

unit cell. The approximation is reasonable since the metal surfaces have a small lattice

constants mismatch of less than 4% with that of graphene, as seen in Table 1. A vacuum

buffer space of at least 12 Ǻ is set.

The geometry optimizations and electronic structure calculations are performed with the

ultrasoft pseudopotentials52

plane-wave basis set with energy cut-off of 350 eV, implemented

in the CASTEP code53

.

Generalized gradient approximation (GGA) of

14

Perdew–Burke–Ernzerhof (PBE) form54

to the exchange-correlation functional is used. To

account for the dispersion interaction between graphene, a DFT-D semiempirical

dispersion-correction approach is adopted55

. During the calculations, the cell shape and the

bottom four layers of metal atoms are fixed. To obtain reliable optimized structures, the

maximum residual force is less than 0.01 eV/Å and energies are converged to within 510-6

eV per atom. The Monkhorst-Pack56

k-point mesh is sampled with a separation of about 0.02

and 0.01 Å-1

in the Brillouin zone, respectively, during the relaxation and electronic

calculation periods. The component of the energy band and the plane-averaged excess

electron density are analyzed via additional calculations based on the plane-wave basis set

with a cut-off energy of 400 eV and the projector-augmented wave (PAW) pseudopotential

implemented in the VASP code57,58

. The electronic structures generated by the two packages

are nearly indistinguishable.

TLG/Ru(0001) interface model is constructed from a slab of six layers of Ru with the

bottom four layers are fixed and a TLG adsorbed on one side. Following the previous work by

Sutter et al.22

, ABA-stacked TLG is strained to match the Ru lattice parameter a = 2.68 Å.

Using the same calculation parameters22

, the ABA-stacked TLG/Ru contact is recalculated by

using the CASTEP and VASP codes, respectively. Namely, ultrasoft pseudopotential52

plane-wave basis set with energy cutoff of 340 eV is used. The local density approximation

(LDA) in the Ceperley-Alder form is used for the exchange and correlation functional59,60

.

The Monkhorst-Pack56

k-point is sampled by a 1515 mesh in the Brillouin zone.

To study how the metallic contacts affect the transport properties of the BLG devices, a

two-probe model made of BLG is built, and the BLG channel is contacted with two Al/Ti

electrodes (source and drain). We perform transport calculations at zero source-drain bias by

using the DFT method coupled with nonequilibrium Green’s function (NEGF) method, which

are implemented in ATK 11.2 package61-63

. Single-zeta (SZ) basis set is used, the real-space

mesh cutoff is 150 Ry., and the temperature is set at 300 K. The local-density-approximation

(LDA)59,60

is employed for the exchange–correlation functional. The electronic structures of

electrodes and central region are calculated with a Monkhorst–Pack56

50 × 1 × 100 and 50 × 1

× 1 k-point grid, respectively.

15

Acknowledgement This work was supported by the National Natural Science Foundation

of China (Nos. 11274016, 51072007, 91021017, 11047018, and 60890193), the National

Basic Research Program of China (Nos. 2013CB932604 and 2012CB619304), Fundamental

Research Funds for the Central Universities, National Foundation for Fostering Talents of

Basic Science (No. J1030310/No. J1103205), Program for New Century Excellent Talents in

University of MOE of China, and Nebraska Research Initiative (No. 4132050400) and DOE

DE-EE0003174 in the United States. J. Zheng also acknowledges the financial support from

the China Scholarship Council.

Author Contributions. The idea was conceived by J. L. The calculation was performed by J.

Z. and Y. W. The data analyses were performed by J. Z., Y. W., L. W., R. Q., and J. L.. Z. N.,

W. M., D. Y., J. S., and Z. G. took part in discussion. This manuscript was written by J. Z., Y.

W., and J. L.. All authors reviewed this manuscript.

Additional Information.

Competing Financial Interests

The authors declare no competing financial interests.

16

Author Information

● Affiliations

State Key Laboratory of Mesoscopic Physics and Department of Physics, Peking

University, Beijing 100871, P. R. China

Jiaxin Zheng, Yangyang Wang, Ruge Quhe, Zeyuan Ni, Dapeng Yu, Junjie Shi,

Zhengxiang Gao, Jing Lu

Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871,

P. R. China

Jiaxin Zheng, Ruge Quhe

Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska

68182-0266

Lu Wang, Wai-Ning Mei

● Corresponding authors

Correspondence to: Jing Lu (jinglu@pku.edu.cn)

17

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21

Table 1. Calculated interfacial distance dC-M, binding energy Eb of per carbon atom, work

functions W, band gap Eg, and Fermi-level shift ΔEf for BLG and ABA- and ABC-stacked

TLG on various metal surfaces. Because the electronic structure of the contacted layer

graphene is strongly perturbed on Ni, Co, Ti, and Pd surfaces, we give the Fermi-level shift

and band gap for the uncontaced single layer graphene of BLG and two graphene layers of

TLG, respectively. exp

hexa is the experimental lattice parameters of the surface unit cells shown

in Figure 1b and 1d, and WM the calculated work functions for various clean metal surfaces.

a Majority-spin band,

b Minority-spin band.

Substrates

exp

hexa

(Å)

WM

(eV)

BLG

ABA-stacked TLG

ABC-stacked TLG

dC-M

(Å)

Eb

(eV)

W

(eV)

Eg

(eV)

ΔEf

(eV)

dC-M

(Å)

Eb

(eV)

W

(eV)

Eg

(eV)

ΔEf

(eV)

dC-M

(Å)

Eb

(eV)

W

(eV)

Eg

(eV)

ΔEf

(eV)

Al 4.96 4.06 3.45 0.057 3.80 0.200 -0.361

3.43 0.035 3.82 0.061 −0.293

3.39 0.039 4.09 0.249 −0.331

Ag 5.00 4.46 3.41 0.052 4.1 0.131 -0.182

3.24 0.033 3.92 0.032 −0.204

3.24 0.035 4.35 0.203 −0.249

Cu 2.56 4.84 3.19 0.063 4.27 0.110 -0.171

3.13 0.051 4.39 0.041 −0.182

3.21 0.047 4.60 0.181 −0.137

Au 4.99 5.17 3.46 0.051 4.89 0.102 0.230

3.44 0.032 4.71 0 0.171

3.43 0.036 4.96 0 0.141

Pt 4.81 5.82 3.53 0.059 5.19 0.113 0.351

3.17 0.037 5.15 0 0.204

3.13 0.039 5.42 0.018 0.145

Ti 5.11 4.20 2.18 0.21 3.89 0 -0.283

2.20 0.188 3.58 0.142 −0.203

2.20 0.208 3.82 0.100 −0.360

Co 2.51 4.97 2.17 0.099 4.33 0

-0.428a

2.05 0.138 4.46

0.177a −0.248a

2.04 0.172 4.15

0.226a −0.278a

-0.381b 0.156b −0.259b 0.160b −0.242b

Ni 2.49 4.95 2.34 0.094 4.32 0

-0.364a

2.13 0.123 4.25

0.191a −0.238a

2.13 0.156 4.40

0.185a −0.247a

-0.280b 0.157b −0.257b 0.229b −0.278b

Pd 4.76 5.33 2.70 0.083 4.74 0.124 -0.160

2.54 0.085 4.88 0.064 −0.104

2.50 0.103 4.82 0.308 −0.220

22

Figure 1: Interfacial structures of B(T)LG on metal substrates. (a) Top and side views of

the most stable configuration for SLG (the green balls)35,36

and BLG on Ni, Co, and Cu (111)

surfaces. (b) Top views of the most stable configuration for SLG35,36

and BLG on Ti (0001)

surface, and Pd, Al, Ag, Au, and Pt (111) surfaces. (c) and (d) The relaxed configurations for

TLG on the corresponding metal substrates with split alignment of the first (innermost)

graphene layer to metals compared to (a) and (b). Red and purple balls denote metal atoms of

the first and rest layers, respectively. Green and gray balls denote the first and second layers

of graphene, respectively. The third (outermost) graphene layer (not shown) is vertically

aligned with the first layer for ABA stacking mode and it has a vector translation (labeled by

a black arrow) with respect to the first layer for ABC stacking mode. dC-M is the equilibrium

distance between the metal surface and the bottom layer graphene. The yellow diamonds

represent unit cells.

23

Figure 2. Band structures of freestanding BLG and BLG physisorbed on Al, Ag, Cu, Au, and

Pt (111) substrates. The Fermi level is set to zero. BLG dominated bands (red) are plotted

against the metal projected bands (green).

24

Figure 3. (a) Calculated Fermi-level shift as a function of WM – WG, the difference between

the clean metal and graphene work functions. WM – WG = 0.4 eV is the cross point from n- to

p-type doping. (b) Schematic of the BLG/metal contacts. E and E1 denote the electric fields

between metal and graphene and between the graphene layers, respectively. (c) Band gap as a

function of ΔEf in BLG physisorbed on the metal surfaces. The red dot-dashed line in (c) is a

boundary of n- and p-type doping region. The black dashed line in (c) is a linear fit to the Eg –

ΔEf data in the n-type doped region. The band gap (green diamond) of the upper layer

graphene for BLG weakly chemisorbed on Pd surface is also given.

25

Figure 4. Band structures of BLG chemisorbed on Ni, Co, and Pd (111) and Ti (0001)

substrates. The Fermi level is set to zero. Green line: metal surface bands; blue line: bands of

the upper layer graphene; red line: bands of the bottom layer graphene.

26

Figure 5. Band structures of ABA- and ABC-stacked TLG physisorbed on Al, Ag, Cu, Au,

and Pt (111) surfaces. The Fermi level is set at zero. TLG-dominated bands (red) are plotted

against the metal projected bands (green). The first and third top panels correspond to the

band structure of freestanding ABA- and ABC- stacked TLG with graphene 22 supercell,

respectively.

27

Figure 6. Calculated Fermi-level shift ΔEf as a function of WM − WG, the difference between

the clean metal and TLG work functions, for (a) ABA- and ABC-stacked TLG physisorbed on

the metal surfaces. (b) Band gap Eg as a function of ΔEf in ABC-stacked TLG physisorbed on

the metal surfaces. The red dash-dot line is the boundary of the n- and p-type doping region.

28

Figure 7. Band structures of ABA- and ABC-stacked TLG chemisorbed on Ti (0001), Co, Ni,

and Pd (111) surfaces. The Fermi level is set at zero. TLG-dominated bands are plotted

against the metal projected bands (green). Blue and red lines depict the bands with weight

projected on the innermost graphene layer and the outer graphene bilayer, respectively. The

labels Maj/Min represent the majority- and minority-spin bands, respectively.

29

(a)

(f)

Figure 8. (a) Two-probe model. The length of the channel is Lch = 9.6 nm. Gray ball: C; blue

ball: Al or Ti. (b) Zero-bias transmission spectrum with Al electrodes. Inset: transmission

spectrum of a freestanding BLG with the same Lch. (c) Zero-bias transmission spectrum of

SLG contacted with Al electrodes with Lch = 9.6 nm. (d) Projected density of states (PDOS) of

BLG contacted with Al electrodes. (e) Zero-bias transmission spectrum of BLG contacted

with Ti electrodes with Lch = 9.6 nm. (f) Transmission eigenstates at E – Ef = –0.6 eV and at k

= (π/3a, 0) with Al and Ti electrodes, respectively. The isovalue is 0.2 a.u..

Source Drain